In recent years, the development of the manufacturing technology for a refrigerator or an air conditioner has been advanced due to a rapid development in the refrigeration technique and air-conditioning technique. Most effort is concentrated on providing a refrigerator or air conditioner with higher efficiency, less volume and lower weight, as well as an improved refrigerant. Meanwhile, the design and technical application for an evaporating heat-exchange tube used in the refrigerator or air conditioner has also been continuously improved. Currently, there are several ways to improve an evaporating heat-exchange tube. One way to improve an evaporating heat-exchange tube is to increase the heat transfer area thereof. 1) To increase the area is to add heat-exchange fins or form heat-exchange fins directly on the outer surface of the evaporating heat-exchange tube. However, adding fins on the outer surface may lead to such a disadvantage that thermal resistance will be developed between the fins and the tube, while heat-exchange fins forming directly on the outer surface are often limited by the machining process and the size of the tube, such that a requirement to transfer heat rapidly may not be well met. 2) To provide a space at the interface of the tube and the refrigerant to promote the formation of a bubble nucleus, such that bubbles are easily formed in said space. Bubbles absorb heat near the tube surface and grow accordingly. Due to the surface tension, these bubbles may leave the tube surface only when their sizes become large enough to overcome the surface tension. A prior art promotion space at the tube surface is relatively large. Therefore, the bubble size needed to overcome the surface tension is also quite large, and the rate of the heat transfer is slowed sown. Meanwhile, this also slows down the formation rate of new bubbles. 3) In prior art evaporating heat-exchange tube, the length for a transitional portion between a smooth surface and a finned surface is about 60 mm. The longer this transitional length is, the more will be incomplete fins, and the more will the refrigeration property be adversely affected.